Common features of \(\exists \mathbb {R}\) -complete problems are their continuous solution space and the nonlinear relations between their variables.
Important \(\exists \mathbb {R}\) -completeness results include the realizability of abstract order types [1]}, [2]} and geometric linkages [3]}, as well as the recognition of geometric segment graphs [4]}, [5]}, unit-disk graphs [6]}, [7]}, and ray intersection graphs [8]}.
More results appeared in the graph drawing community [9]}, [10]}, [11]}, [12]}, regarding polytopes [13]}, [14]}, the study of Nash-equilibria [15]}, [16]}, [17]}, [18]}, [19]}, training neural networks [20]}, [21]}, matrix factorization [22]}, [23]}, [24]}, [25]}, or continuous constraint satisfaction problems [26]}.
In computational geometry, we would like to mention the art gallery problem [27]}, [28]} and covering polygons with convex polygons [29]}.
